I thoroughly read all three establishment orders and found no clause stating only one could be earned. I've seen photos of award ceremonies for all three medals and have yet to see anybody wearing more than the one.
Now, having said that, the award criteria for the Medal "Participant in Military Operations in Syria" means it would logically be awarded to anybody in theatre, even the liberators of Palmyra, and later the EOD personnel. I guarantee you I'll keep a sharp eye out in the future to see if I can find a photo of a Russian serviceman wearing more than one.